Open AccessSpectral theory for self-adjoint linear relation (SALR) on a Hilbert space and its application in homogenous abstract cauchy problem
Author(s) -
Susilo Hariyanto,
Ratna Kumala Sari,
Farikhin,
YD Sumanto,
Solikhin - Solikhin,
Abdul Aziz
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1321/2/022070
Subject(s) - eigenvalues and eigenvectors , mathematics , spectral theory , hilbert space , cauchy distribution , linear map , operator (biology) , inverse , self adjoint operator , mathematical analysis , spectrum (functional analysis) , space (punctuation) , relation (database) , pure mathematics , quantum mechanics , physics , computer science , biochemistry , chemistry , geometry , repressor , database , transcription factor , gene , operating system
A spectral theory studies eigenvalues and eigenvectors of SALR on H. SALR on Hilbert space H is a linear relation satisfying A = A*. Many applications of SALR on quantum theory, such as the homogenous abstract Cauchy problem.If M is an operator that has an inverse then eigenvalues and eigenvectors are easily determined, but If M is an operator that does not have an inverse then eigenvalues and eigenvectors are quite difficult determined. One way that can be done is to use a linear relation. Furthermore, there are some properties of spectral theoryof linear operator that can not apply to SALR. This paper aims to give a spectral theory for SALR and its application in a homogenous abstract Cauchy problem.